5. Arithmetics of Geometric Shape

  1. Pijush K. Ghosh1 and
  2. Koichiro Deguchi2

Published Online: 28 JAN 2010

DOI: 10.1002/9780470823095.ch5

Mathematics of Shape Description: A Morphological Approach to Image Processing and Computer Graphics

Mathematics of Shape Description: A Morphological Approach to Image Processing and Computer Graphics

How to Cite

Ghosh, P. K. and Deguchi, K. (2008) Arithmetics of Geometric Shape, in Mathematics of Shape Description: A Morphological Approach to Image Processing and Computer Graphics, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470823095.ch5

Author Information

  1. 1

    National Centre for Software Technology (now Centre for Development of Advanced Computing), India

  2. 2

    Graduate School of Information Sciences, Tohoku University, Japan

Publication History

  1. Published Online: 28 JAN 2010
  2. Published Print: 26 MAR 2008

ISBN Information

Print ISBN: 9780470823071

Online ISBN: 9780470823095

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Keywords:

  • geometric shape arithmetics;
  • motivation for shape arithmetic;
  • morphology and theory of numbers;
  • Minkowski addition ⊕(dilation) and Minkowski decomposition (erosion);
  • morphological system and integer number system resemblance;
  • boundary representation by support functions for morphological operations;
  • geometric operations and support functions;
  • convex polygons and morphological operations;
  • Minkowski decomposition - and supporting function vector means;
  • convex polyhedra domain

Summary

This chapter contains sections titled:

  • The Motivation for a Shape Arithmetic

  • Morphology and the Theory of Numbers

  • Boundary Representation by Support Functions for Morphological Operations

  • Geometric Operations by Means of Support Functions

  • Morphological Operations on Convex Polygons

  • In the Domain of Convex Polyhedra